#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Blackbody - Planckian Radiator
==============================
Defines objects to compute the spectral radiance of a planckian radiator and
its spectral power distribution.
See Also
--------
`Blackbody Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/colorimetry/blackbody.ipynb>`_
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.colorimetry import (
DEFAULT_SPECTRAL_SHAPE,
SpectralPowerDistribution)
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2017 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = ['C1',
'C2',
'N',
'planck_law',
'blackbody_spectral_radiance',
'blackbody_spd']
C1 = 3.741771e-16 # 2 * math.pi * PLANCK_CONSTANT * LIGHT_SPEED ** 2
C2 = 1.4388e-2 # PLANCK_CONSTANT * LIGHT_SPEED / BOLTZMANN_CONSTANT
N = 1
[docs]def planck_law(wavelength, temperature, c1=C1, c2=C2, n=N):
"""
Returns the spectral radiance of a blackbody at thermodynamic temperature
:math:`T[K]` in a medium having index of refraction :math:`n`.
Parameters
----------
wavelength : numeric or array_like
Wavelength in meters.
temperature : numeric or array_like
Temperature :math:`T[K]` in kelvin degrees.
c1 : numeric or array_like, optional
The official value of :math:`c1` is provided by the Committee on Data
for Science and Technology (CODATA) and is
:math:`c1=3,741771x10.16\ W/m_2` *(Mohr and Taylor, 2000)*.
c2 : numeric or array_like, optional
Since :math:`T` is measured on the International Temperature Scale,
the value of :math:`c2` used in colorimetry should follow that adopted
in the current International Temperature Scale (ITS-90)
*(Preston-Thomas, 1990; Mielenz et aI., 1991)*, namely
:math:`c2=1,4388x10.2\ m/K`.
n : numeric or array_like, optional
Medium index of refraction. For dry air at 15°C and 101 325 Pa,
containing 0,03 percent by volume of carbon dioxide, it is
approximately 1,00028 throughout the visible region although
*CIE 15:2004* recommends using :math:`n=1`.
Returns
-------
numeric or ndarray
Radiance in *watts per steradian per square metre*.
Notes
-----
- The following form implementation is expressed in term of wavelength.
- The SI unit of radiance is *watts per steradian per square metre*.
References
----------
.. [1] CIE TC 1-48. (2004). APPENDIX E. INFORMATION ON THE USE OF
PLANCK’S EQUATION FOR STANDARD AIR. In CIE 015:2004 Colorimetry,
3rd Edition (pp. 77–82). ISBN:978-3-901-90633-6
Examples
--------
>>> # Doctests ellipsis for Python 2.x compatibility.
>>> planck_law(500 * 1e-9, 5500) # doctest: +ELLIPSIS
20472701909806.5...
"""
l = np.asarray(wavelength)
t = np.asarray(temperature)
p = (((c1 * n ** -2 * l ** -5) / np.pi) *
(np.exp(c2 / (n * l * t)) - 1) ** -1)
return p
blackbody_spectral_radiance = planck_law
[docs]def blackbody_spd(temperature,
shape=DEFAULT_SPECTRAL_SHAPE,
c1=C1,
c2=C2,
n=N):
"""
Returns the spectral power distribution of the planckian radiator for given
temperature :math:`T[K]`.
Parameters
----------
temperature : numeric
Temperature :math:`T[K]` in kelvin degrees.
shape : SpectralShape, optional
Spectral shape used to create the spectral power distribution of the
planckian radiator.
c1 : numeric, optional
The official value of :math:`c1` is provided by the Committee on Data
for Science and Technology (CODATA) and is
:math:`c1=3,741771x10.16\ W/m_2` *(Mohr and Taylor, 2000)*.
c2 : numeric, optional
Since :math:`T` is measured on the International Temperature Scale,
the value of :math:`c2` used in colorimetry should follow that adopted
in the current International Temperature Scale (ITS-90)
*(Preston-Thomas, 1990; Mielenz et aI., 1991)*, namely
:math:`c2=1,4388x10.2\ m/K`.
n : numeric, optional
Medium index of refraction. For dry air at 15°C and 101 325 Pa,
containing 0,03 percent by volume of carbon dioxide, it is
approximately 1,00028 throughout the visible region although
*CIE 15:2004* recommends using :math:`n=1`.
Returns
-------
SpectralPowerDistribution
Blackbody spectral power distribution.
Examples
--------
>>> from colour import STANDARD_OBSERVERS_CMFS
>>> cmfs = STANDARD_OBSERVERS_CMFS['CIE 1931 2 Degree Standard Observer']
>>> print(blackbody_spd(5000, cmfs.shape))
SpectralPowerDistribution('5000K Blackbody', (360.0, 830.0, 1.0))
"""
wavelengths = shape.range()
return SpectralPowerDistribution(
name='{0}K Blackbody'.format(temperature),
data=dict(
zip(wavelengths,
planck_law(
wavelengths * 1e-9, temperature, c1, c2, n))))